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Properties

Label 26010m
Number of curves $2$
Conductor $26010$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 26010m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26010.d2 26010m1 \([1, -1, 0, 36360, -7086420]\) \(302111711/1404540\) \(-24714690068016540\) \([2]\) \(184320\) \(1.8279\) \(\Gamma_0(N)\)-optimal
26010.d1 26010m2 \([1, -1, 0, -405810, -88534134]\) \(420021471169/50191650\) \(883186718607061650\) \([2]\) \(368640\) \(2.1745\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26010m have rank \(0\).

Complex multiplication

The elliptic curves in class 26010m do not have complex multiplication.

Modular form 26010.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 2 q^{7} - q^{8} + q^{10} + 4 q^{13} + 2 q^{14} + q^{16} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.